Reactions of HOCl + HCl + nh 2 O and HOCl + HBr + nh 2 O

Transcription

1 7850 J. Phys. Chem. A 2002, 106, Rections of HOCl + HCl + nh 2 O nd + nh 2 O Andres F. Voegele, Christofer S. Tutermnn, Thoms Loerting, nd Klus R. Liedl* Institute of Generl, Inorgnic nd Theoreticl Chemistry, UniVersity of Innsbruck, Innrin 52, A-6020 Innsbruck, Austri ReceiVed: Jnury 25, 2002; In Finl Form: April 15, 2002 We present rection rtes for the conversion of HOCl by HCl nd HBr into Cl 2 nd BrCl, respectively, supported by n ) 0, 1, 2, nd 3 wter molecules. The rection rtes were determined using cnonicl, vritionl trnsition-stte theory including tunneling corrections for motion long the rection coordinte. Wheres the potentil energy surfce between rectnts, trnsition stte, nd products ws generted with the hybrid density functionl theory B3LYP/6-31+G(d), the rection brrier ws determined with the recently developed MPW1K/ 6-31+G(d,p) hybrid density functionl theory, method tht ws especilly designed to evlute rection brriers. Within the used density functionl theory frmework, the rection rtes of HOCl with HBr re severl orders of mgnitude higher thn the rection rtes with HCl. On ice-like clusters, both types of rections proceed fster by severl orders of mgnitude thn in the gs phse or when supported by only one or two wter molecules. Knowledge of the rection rtes is importnt in estimting which rection will occur under strtospheric conditions in the course of ozone depletion. 1. Introduction Ozone depletion in the strtosphere over Antrctic nd Arctic is cused to gret extent by ctlytic rections of ozone with chlorine rdicls nd to smller extent by rections with bromine rdicls. 1-5 Hlogen toms re stored in nerly inert reservoir species (ClONO 2, HCl, nd HBr) nd relesed into more ctive forms through severl rections tht occur minly on polr strtospheric clouds (PSC). 6 One of the min rections is the hydrolysis of ClONO 2 tht produces HOCl. There re two common wys in which HOCl cn rect further. First, if HOCl is desorbed from the PSC, it will be quickly photolyzed by sunlight where rective species such s the HO nd Cl rdicls re formed. Second, in the presence of HCl or HBr, it is very likely tht HOCl rects with one of these molecules. 7,8 HOCl + HCl Cl 2 + H 2 O (1) BrCl + H 2 O (2) Both rections 1 nd 2 re known to occur minly heterogeneously in the strtosphere wheres the homogeneous gs-phse rections re considered to be more or less unimportnt Rections 1 nd 2 re crucil steps for the finl relese of rective hlogen species in the strtosphere. Becuse of the gret importnce of both rections, there re not only experimentl but lso severl theoreticl studies on the rection of HOCl with HCl Aprt from studies investigting the rection, there re lso studies on the interctions of HCl nd HOCl 16,21-24 with wter/ice clusters, respectively. Most of the theoreticl studies hve concentrted on the influence of () wter molecules on the dsorption behvior of single species, (b) wter molecules on the rection brrier, 14,15 nd (c) n nion 12 on the rection brrier. * Corresponding uthor. E-mil: Klus.Liedl@uibk.c.t. Tel.: Fx: Present ddress: Deprtment of Erth, Atmosphere nd Plnetry Sciences, Msschusetts Institute of Technology, 77 Msschusetts Avenue, Cmbridge, Msschusetts Kroes nd Clry 16 determined dsorption energies for HCl nd HOCl on ice with trjectory methods wheres Geiger et l. 21 determined the dsorption energies by using wter clusters nd b initio methods. An extended study of the HOCl dsorption on model ice ws performed by Brown nd Doren 23 using cluster of 26 wter molecules. Liu et l. performed b initio moleculr dynmics simultions of the rection HCl + HOCl on n ice surfce using plne wves in their density functionl theory pproch. 13 In detiled study, Xu 14 investigted the rection of HOCl with HCl in wter clusters of different sizes with b initio methods. Xu reports tht the rection brrier is lowered systemticlly by including ctive wter molecules in the rection. Active in this respect mens tht the wter molecules tke prt ctively in the rection serving s proton donor nd cceptor in proton-trnsfer mechnism nd tht wter molecules do not serve only s specttors. In the course of n unctlyzed rection (n ) 0), the brrier is 55.3 kcl mol -1 wheres for the wter-ctlyzed rections it decreses to 48.1 kcl mol -1 (n ) 1), 16.1 kcl mol -1 (n ) 2), nd 14.4 kcl mol -1 (n ) 3) t the MP2//HF/6-31G(d) level of theory. A proposed mechnism involving four wter molecules hs brrier of 45 kcl mol -1, which reflects the fct tht simple increse in the number of ctive wter molecules is not sufficient to obtin n lmost brrierless rection, s would be expected in solution. Xu lso showed tht inclusion of so-clled structurl or specttor wter molecules lowers the brrier significntly, down to n lmost brrierless sitution. 14 To the best of our knowledge, there hs been no theoreticl study on the rection of, nd thus no comprison between the rections HOCl + HCl nd hs been performed. In this study, we ddress both rections nd mke comprison between them using b initio methods nd vritionl trnsition-stte theory to clculte rection rtes. Clculting rection rtes mkes it possible to quntify the rection rte difference between the gs-phse rection nd the heterogeneous rection on n ice surfce (described by wter clusters). Finlly, we wnt to evlute the performnce of different b initio methods for the described rections /jp CCC: $ Americn Chemicl Society Published on Web 07/26/2002

2 Rections of HOCl + HX + nh 2 O(X) Cl, Br) J. Phys. Chem. A, Vol. 106, No. 34, Methods 2.1. Sttionry Points. Sttionry points were clculted with two different hybrid density functionl theory (DFT) methods, nmely, B3LYP/6-31+G(d) 25 nd MPW1K/6-31+G(d,p). 26 The nture of these sttionry points ws confirmed by vibrtionl nlysis. For optimiztion of the sddle point, we employed the three-structure qudrtic synchronous trnsit-guided pproch. 27 Becuse clssicl DFT nd hybrid DFT methods such s B3LYP tend to underestimte rection brriers, 26,28-30 we employed the recently developed modified Perdew-Wng 1-prmeter model for kinetics (MPW1K) hybrid DFT method of Lynch et l. 26 This method ws especilly designed for the purpose of determining rection brriers to be pplied to rection rte constnt clcultions. MPW1K uses modified Perdew- Wng grdient-corrected correltion functionl 26,31-33 nd 42.8% Hrtree-Fock exchnge. Within test set of 40 rection brriers, MPW1K hs men signed, men unsigned, nd rootmen-squre errors of -1.2, 1.6, nd 2.1 kcl mol -1, respectively, compred to experiment; therefore, this method is significntly better thn the more commonly used BH&HLYP, B3LYP, or MPW1PW91 26,34 methods. However, this test set contins minly hydrocrbon rections, only four rections contining Cl species, nd no rections contining Br species. Becuse MPW1K hs not been optimized to one of the title rections or t lest very similr rection, we hve to consider the fct tht the results might devite from the experimentl results by few kcl mol -1. MPW1K ws optimized using the 6-31+G(d,p) bsis set; therefore, the sme bsis set will be used throughout this study. Additionlly, we employed high-level methods to evlute more ccurte rection brriers. To describe rection rtes by trnsition-stte theory, it is necessry to evlute precise rection brriers becuse of the exponentil reltionship between the rection brrier nd rection rte. Therefore, we used Gussin-2 theory [G2(MP2)] 35,36 nd Gussin-3 theory [G3 nd G3(MP2)] 37,38 for some of the systems studied. Both the Gussin-2 nd Gussin-3 theories employ qudrtic configurtion interction with single, double, nd perturbtionl triple excittions [QCISD(T)] but with different bsis sets. G2(MP2) uses the triple-ζ 6-311G(d,p) bsis set, which is remrkbly lrger thn the double-ζ 6-31G(d) bsis set used in G3(MP2). The qulity of the QCISD(T) clcultion in G3 nd G3(MP2) is significntly lower thn in G2(MP2). Deficiencies in the bsis set re ccounted for in both G2 nd G3 theory with bsis set extrpoltion method employing MP2 nd MP4, respectively, which is explined in detil in the originl work by Pople nd co-workers Briefly, in G2(MP2), one dds the difference between MP2/6-311+G(3df,2p) nd MP2/6-311G(d,p) to the QCISD(T)/6-311G(d,p) clcultion nd gets good pproximtion for QCISD(T)/6-311+G(3df,2p). G3(MP2) uses the difference between the energy clcultions on the MP2/G3MP2lrge nd MP2(full)/6-31G(d) levels of theory (the G3MP2lrge bsis set is modified G(3df,2p) bsis set; for detils, see Curtiss et l. 37,38 ). In given test set (G2/97), G3(MP2) performs slightly better thn G2(MP2) nd is computtionlly less expensive. 38 We wnted to compre the methods to clculte rection brriers nd rection energies. As nother high-level method, we used coupled cluster theory with single, double, nd perturbtionl triple excittions [CCSD(T)/ug-cc-pVDZ] 39 on the geometries we obtined t the MP2/ug-cc-pVDZ 40,41 level of theory [CCSD(T)/ug-cc-pVDZ//MP2/ug-cc-pVDZ]. To test for n pproprite choice of the HF reference wve function, the performnce of CCSD(T)/ug-cc-pVDZ ws tested by the u 1 dignostic Rection Pth. By strting from the trnsition stte, the rection pth ws creted s the steepest descent pth in mssscled coordintes where the scling mss of 1 mu ws used. To crete this so-clled minimum-energy pth (MEP) or intrinsic rection coordinte (IRC), the Pge-McIver locl qudrtic pproximtion lgorithm 43 nd B3LYP/6-31+G(d) were used t step size of Bohr (0.026 Å). Distnces on the potentil energy surfce from the trnsition stte re denoted s, where s is positive on the product side nd negtive on the educt side. Every third point long the potentil energy surfce s second derivtives nd prtition functions ws clculted. The pth ws clculted on both sides of the trnsition stte until stble minimum structures were reched (i.e., when the grdient hd lmost vnished). B3LYP in generl describes geometries nd energy hypersurfces well but underestimtes the height of rection brriers (s mentioned previously). Therefore, we interpolted the B3LYP/6-31+G(d) hypersurfce to the energy vlues of the sttionry points determined t the MPW1K/6-31+G(d,p) level of theory. Clculting the rection pth nd thus the rection rtes on the bsis of two different levels of theory is termed dul-level direct dynmics, nd the interpoltion procedure is clled vritionl trnsition-stte theory with interpolted corrections. The shorthnd nottion for this procedure is MPW1K/6-31+G(d,p)///B3LYP/6-31+G(d), nd the interpoltion procedure is bsed on logrithmic procedure Rection Rtes nd Quntum Mechnicl Tunneling. Rection rtes were obtined using trnsition-stte theory (TST) 45 s implemented in Polyrte, version ,47 Theoreticl detils nd equtions cn be found elsewhere; 45,48-54 here we give just short description of some of the detils. A vritionl pproch for TST with cnonicl ensemble ws used to obtin rte constnt k CVT (CVT ) cnonicl vritionl TST) tht ws minimized with respect to brrier crossings. When ll bound degrees of freedom re described quntum mechniclly, motion long the rection coordinte cnnot be treted quntum mechniclly. Therefore, quntum mechnicl effects (minly tunneling effects) long the rection coordinte re well pproximted by semiclssicl methods to evlute trnsmission probbilities. Inclusion of the quntum mechnicl effects on the rection rte constnt is crried out by multiplying the rte constnt k CVT by ground-stte trnsmission coefficient κ. The trnsmission coefficient is evluted by different methods tht consider tht in the course of the rection the system tunnels long shorter pths tht re more demnding in terms of energy. The methods we consider re the crude Wigner tunneling correction, the smll curvture tunneling (SCT) pproch, nd the lrge curvture tunneling (LCT) pproch. The Wigner correction, which ws developed in 1932, 55 is bsed only on the imginry frequency determined t the trnsition stte nd does not include informtion bout the rection pth. SCT is considered by mens of the centrifugl dominnt smll-curvture semiclssicl dibtic ground-stte tunneling method ccording to the concept of Mrcus nd Coltrin The LCT correction ssumes tht tunneling occurs through series of stright line connections between the educt nd the product vlley. Polyrte employs the lrge curvture ground-stte pproximtion version 4 (LCG4) 59 for LCT. Depending on the curvture of the rection pth nd the temperture, either SCT or LCT becomes predominnt; thus, one uses the mximum of these methods to evlute the tunneling corrections nd multiplies it by k CVT. This pproch is termed microcnonicl optimized multidimensionl tunneling (µomt).

3 7852 J. Phys. Chem. A, Vol. 106, No. 34, 2002 Voegele et l. TABLE 1: Selected Rection Brriers for the Rections HOCl + HCl nd Ctlyzed by n Wter Molecules t Different Levels of Theory rection brrier (kcl mol -1 ) HOCl + HCl MP2 CC G2(MP2) G3(MP2) G3 n ) (0.075) n ) 1() (0.059) n ) n ) (0.079) 48.0 n ) 1() 46.1 CC is our shorthnd nottion for CCSD(T)/ug-cc-pVDZ//MP2/ ug-cc-pvdz, nd MP2 stnds for MP2/ug-cc-pVDZ. Numbers in prentheses beside the coupled-cluster vlues re the u 1 vlues determined for the trnsition stte. Using the ug-cc-pvtz insted of the DZ bsis set did not improve u 1 significntly. Note tht we did not clculte ll systems t the different levels of theory becuse of the unsuccessful description of the multideterminnt chrcter, s mentioned in the text. TABLE 2: Rection Brriers for the Rections HOCl + HCl nd Ctlyzed by n Wter Molecules t Different Levels of Theory HOCl + HCl B3LYP/ 6-31+G(d) rection brrier (kcl mol -1 ) MPW1K/ 6-31+G(d,p) MP2//HF/ 6-31G(d) 14 n ) b b n ) 1 () b 54.7 n ) 1 (b) b b n ) b b n ) b b n ) b 44.4 n ) b 44.6 n ) b 0.76 n ) b 0.75 Energies determined t the MP2//HF/6-31G(d) level re tken from Xu. 14 b Corrected for zero-point energy (ZPE). 3. Results nd Discussion 3.1. Evlution of the Methods. We determined most of the rection brriers for the title rections t severl levels of theory (Tble 1 nd Tble 2 give brief summry). Unfortuntely, there re lrge differences between most of the methods. G2(MP2), G3(MP2), nd G3 differ by up to lmost 30 kcl mol -1, clerly indicting tht these methods fil to reproduce rection brriers for the described systems within chemicl ccurcy. We used the u 1 dignostic on the coupled-cluster [CCSD(T)/ug-cc-pVDZ//MP2/ug-pVDZ] clcultions nd evluted u 1 vlues for trnsition sttes tht were clerly lrger thn 0.04 nd sometimes s lrge s u 1 vlues of tht size indicte tht the reference wve function does not describe the system stisfctorily nd tht multideterminnt pproch is needed. Becuse both the coupled-cluster nd the Gussin pproches re bsed on single-determinnt HF wve functions, they suffer from the sme error. Therefore, ccurte multideterminnt methods should be employed, which, considering the number of different rections studied, would be too timeconsuming. 34 We did not evlute ll of the rection brriers t the higher levels becuse these clcultions would lso be too time-consuming, nd results of high qulity cnnot be expected for the lrger clusters. We investigted the chnge in tom-tom distnces between the Cl tom of HOCl, the Cl tom of HCl, nd the Br tom of HBr between the rectnt nd trnsition sttes t different levels TABLE 3: Rection Energies for the Rections HOCl + HCl nd Ctlyzed by n Wter Molecules t Different Levels of Theory HOCl + HCl B3LYP/ 6-31+G(d) rection energy (kcl mol -1 ) MPW1K/ 6-31+G(d,p) MP2//HF/ 6-31G(d)[14] n ) b b n ) 1 () b n ) 1 (b) b b n ) b b n ) b b n ) b n ) b n ) b n ) b Energies determined t the MP2//HF/6-31G(d) level re tken from Xu. 14 b Corrected for zero-point energy (ZPE). TABLE 4: Chnge of Cl-Cl nd Cl-Br Distnce, Respectively, between the Rectnt nd Trnsition Stte Determined t Different Levels of Theory bond length Cl-Cl/Br (Å) HOCl + HCl B3LYP MPW1K MP2 G2(MP2) n ) (40.7) (54.7) (51.9) (35.3) n ) 1 () (41.7) (54.7) (54.3) (62.1) n ) 1 (b) (25.7) (33.1) n ) (6.51) (9.74) (13.6) n ) (4.10) (3.28) n ) (31.6) (44.4) (44.1) (48.0) n ) 1 () (32.6) (44.6) (46.1) n ) (0.86) (0.76) n ) (0.15) (0.75) Within ech row, the brrier decreses with decresing Cl-Cl/Br distnce. of theory (see Tble 4). A slight trend of n incresing brrier with n incresing chnge in tom-tom distnces could be observed both within given set of rections (i.e., rows of Tble 4) nd within given method (i.e., columns of Tble 4). This trend holds, t lest generlly, between the B3LYP nd MPW1K results, mostly between the DFT nd G2(MP2) results, but not with MP2. Thus, the brrier height is very sensitive to the geometry of the studied rections, so bd choice of geometry within given rection yields bd results for the brrier height. Becuse B3LYP underestimtes rection brriers, we used the MPW1K/6-31+G(d,p) brriers tht re lrger thn the B3LYP brriers for most cses (except for HCl nd n ) 3 nd HBr nd n ) 2, 3). The MPW1K method ws optimized by Lynch et l. 30,34 to predict rection brriers for kinetic purposes. The vlues determined with MPW1K were chosen becuse coupled-cluster nd Gussin methods filed to predict the rection brriers nd re so computtionlly expensive tht ll of the systems could not be studied. Additionlly, the MPW1K results re very encourging becuse they re in much better greement with the MP2/ug-cc-pVDZ vlues thn with vlues from other pproches. Possibly, the perturbtionl nd the MPW1K pprochs re better choices for this system thn the other methods tht ctully seem plusible becuse both methods use different pproch thn the other post Hrtree-Fock methods we used. 60,61 Rection brriers re crucil for predicting kinetic properties; therefore, one hs to be wre tht within the ccurcy of MPW1K the error limit is few kcl mol -1. Considering

4 Rections of HOCl + HX + nh 2 O(X) Cl, Br) J. Phys. Chem. A, Vol. 106, No. 34, Figure 1. Clssicl potentil energy curve (or minimum-energy pth; s) nd vibrtionlly dibtic ground-stte potentil energy curve ( ) s function of the rection coordinte s clculted t the B3LYP/ 6-31+G(d) level of theory interpolted to MPW1K/6-31+G(d,p) energies. Left: HOCl + HCl + nh 2O strting from n ) 0 (top) to n ) 3 (bottom); right: + nh 2O. devition of only between 1 nd 2 kcl mol -1, we hve to ssume tht the error in terms of rection rtes is bout 1 to 2 orders of mgnitude between 200 nd 300 K. The rection rtes determined in this study will therefore provide primrily qulittive picture wheres quntittive properties should be considered to ber n error of few orders of mgnitude. Becuse our gols re to estimte which of the two rections is fster nd to pproximte the difference between the gs-phse nd the surfce-ctlyzed rections, our results will give very good picture of which rection will hppen under different conditions Sttionry Points nd Rection Mechnisms HOCl + HCl. We determined sttionry points for the rection of HOCl + HCl with n ) 0, 1, 2, nd 3 wter molecules (see Figure 2). The structure of the pure HOCl HCl complex, representing the gs-phse rection, is chrcterized by hydrogen bond, where HCl serves s proton donor nd HOCl, s proton cceptor. In the course of the rection, HCl protonizes HOCl nd forms H 2 OCl + Cl - -like complex t the trnsition stte tht in the following step forms the products Cl 2 nd H 2 O. The rection brrier is 54.7 kcl mol -1 t the MPW1K/6-31+G(d,p) level of theory, which is in excellent greement with 55.3 kcl mol -1 (with zero-point energy, ZPE) s reported by Xu 14 (brriers nd rection energies re summed up in Tbles 1, 2, nd 3), yet the geometries of the rectnt complex determined in this study differ from the ones determined previously. 14,13 Wheres Liu et l. 13 report vn der Wls complex where the two chlorine toms re closest, Xu 14 reports complex where the O-Cl bond is prllel to the H-Cl bond. Zhou nd Liu 15 report complex tht is more similr to the one determined in this study, where hydrogen bond is formed between the oxygen tom nd H-Cl. (Geometricl detils nd comprison with previous studies re given s Supporting Informtion) HOCl + HCl + 1H 2 O. We found two different locl minimum structures for the HOCl HCl H 2 O complex tht we termed () nd (b) (see Figure 2). Complex () is the lowerlying minimum compred to (b), with n energy difference of 5.0 kcl mol -1. At 200 K, the rtio of complex () to (b) is pproximtely The rection brriers for the two processes re 54.7 () nd 33.1 (b) kcl mol -1, respectively. Assuming tht both complexes re present, rection chnnel (b) would be fster by bout 15 to 20 orders of mgnitude in the temperture rnge from 200 to 300 K. The rection complex determined by Xu 14 resembles our (b) mechnism but is still slightly different. The brrier is higher thn in chnnel (b), nd the rection energy is lower (see Tbles 2 nd 3) (the geometries re compred in Supporting Informtion). In both chnnel () nd chnnel (b), the wter molecule cts s proton shuttle tht is responsible for so-clled wtermedited proton trnsfer. Becuse the brrier of chnnel () is s high s the rection without n dditionl wter molecule, this mechnism will ply no role in the gs phse becuse it is more likely tht complex of two molecules rther thn complex of three molecules will form HOCl + HCl + 2H 2 O. In the course of the rection HOCl + HCl with two ctlytic wter molecules, we cn lso observe proton-shuttle mechnism. Both wter molecules re directly involved in the rection. HCl protontes neighboring wter molecule, nd this molecule in turn trnsfers one of its own protons to the second wter molecule, which dontes one of its protons to HOCl. Finlly, this results in net seprtion of Cl - nd H 2 OCl + t the trnsition stte tht is similr to tht in the unctlyzed rection. The ctlytic effect of the two wter molecules is enormous becuse the brrier is lowered from 54.7 to 9.7 kcl mol -1.Xu 14 found brriers tht were pproximtely 9.5 nd 6.4 kcl mol -1 higher thn the brriers we found even though the structures re very similr HOCl + HCl + 3H 2 O. Finlly, we investigted mechnism for the rection of HOCl with HCl involving three wter molecules. As shown in Figure 2, the rection mechnism is very similr to the mechnism occurring on hexgonl ice surfce (see Figure 3). By lso tking into ccount the fct tht this rection is lmost brrierless (3.3 kcl mol -1 ), we cn ssume tht this rection is representtive of the surfce rection on ice. Even though on rel ice surfce there would be more wter molecules surrounding the rection complex, we think from mechnistic point of view tht the rection is described sufficiently. As demonstrted by Xu, 63 the mechnisms found so fr involving more thn three ctive wter molecules do not occur. Other wter molecules only stbilize the complex but do not prticipte during the rection. The rection tkes plce on surfce; therefore, solvtion effects influence the wter molecules involved in the rection. Yet, HOCl nd HCl, which re locted t the surfce, 62 re not influenced very much by the solvtion effect of other wter molecules. The mechnism for the rection involving three wter molecules proceeds similrly to the bove-mentioned mechnisms where the HCl proton is trnsferred to the first wter molecule, which shuttles one of its own protons to the next wter molecule nd so forth. Even though the bond length of HCl in the clusters of different size increses with the number of wter

5 7854 J. Phys. Chem. A, Vol. 106, No. 34, 2002 Voegele et l. Figure 2. Qulittive representtion of the sttionry points of the rection HOCl + HCl supported by n ) 0, 1, 2, nd 3 wter molecules. The rections with n ) 0, 1, 2, nd 3 wter molecules re nlogous except for mechnism (1b), which could not be found for HBr becuse of the nonconvergence of the trnsition stte. Figure 3. Schemtic representtion of the rection complex of HOCl nd HCl on hexgonl ice surfce. HCl dsorbs perpendiculrly on the ice surfce with its hydrogen bond oriented towrd surfce oxygen tom. HOCl dsorbs on the ice surfce forming hydrogen bridge between the oxygen tom nd dngling hydrogen of the ice surfce. This is the most likely complex on hexgonl ice surfce. The formed complex of HOCl HCl ice is lmost identicl to the mechnism shown in Figure 2 for the mechnism with three wter molecules. molecules involved, we find no Cl - ion in the rectnt stte. This is in greement with the study of Xu, 14 which lso reported no dissocition of HCl in clusters of tht size. Similr to the n ) 2 cse, the rection brrier reported by Xu is much higher (10 kcl mol -1 ) thn our brrier even though the geometries re not significntly different (see Supporting Informtion). The brrier reported by Zhou nd Liu 15 is higher thn ours, but becuse they employed different model for the ice ctlyztion, the different result is not surprising nh 2 O. Qulittively, the picture for is lmost the sme s for the rections involving HCl. All mechnisms were found to be identicl except for mechnism (1b), where the geometry of the trnsition stte did not converge. Becuse of the different size of the bromine tom compred to the chlorine tom, bond lengths nd ngles differ little (see Supporting Informtion). Quntittively, the result is different from the HCl cses becuse the rection brriers re significntly lower (see Tble 2). The mechnisms involving HBr obey trend of significntly lower rection brriers thn those mechnisms involving HCl. The cse for n ) 2 is lmost brrierless, with n energy difference between the educt nd trnsition stte of only 0.76 kcl mol -1. A third ctlytic wter molecule (n ) 3) does not lower the rection brrier (0.75 kcl mol -1 ); therefore, we ssume tht there re two importnt mechnisms for this rection on n ice surfce. The ZPEcorrected brrier for n ) 3 is slightly negtive t the B3LYP/ 6-31+G(d) level, yet when inspecting the potentil energy curve (see Figure 1), we find tht even though the brrier is negtive t the trnsition stte there is mximum in the potentil energy curve off the clssicl trnsition stte. The mximum of G q is temperture-dependent nd is crucil to the determintion of

6 Rections of HOCl + HX + nh 2 O(X) Cl, Br) J. Phys. Chem. A, Vol. 106, No. 34, Figure 4. Schemtic representtion of the rection complex of HOCl nd HBr on hexgonl ice surfce. The mechnism for the cse with three ctive wter molecules is identicl to the mechnism for HOCl + HCl (see Figure 3). Additionlly, mechnism with two ctive wter molecules might occur, which is shown schemticlly in the lower right corner. This mechnism is likely to be importnt for conditions with high surfce coverge with different molecules. the rection rte. We found, however, tht G q t the generlized trnsition stte 49 is positive for ny rection t ny temperture nd tht G q is >RT (even though only by 300 cl mol -1 for n ) 3 nd T ) 100 K, thus the VTST pproch is still pplicble lthough the result should be used with cre). When following the MEP from the trnsition stte, we found no stble intermedites in ny of the rections even though the grdient of the rection is very smll. In both the HCl nd HBr rections, the protons re trnsferred synchronously but concertedly. From the mechnistic point of view, the rections with n ) 2 nd 3 might occur on hexgonl ice (see Figure 2). In Figure 4, we show schemticlly how the rections of HOCl with HBr might occur on n ice surfce Rection Rtes nd Quntum Mechnicl Tunneling. Previous studies on the HOCl + HCl system hve described only rection brriers but not rection rtes. However, the brrier between two rections is not sufficient for the estimtion of differences in rection rtes even if we re interested only in qulittive nd not quntittive picture. An ccurte clcultion of rte constnts for rections involving hydrogen tom trnsfer requires quntum mechnicl tretment of the motion long the rection coordinte. This in turn requires more knowledge of the potentil energy surfce thn just the brrier height. It turns out tht tunneling cn increse the rection rte by mny orders of mgnitude if there is t lest one proton trnsfer involved. Therefore, we determined the tunneling contributions on the rection rtes for the described rections. Figure 5 shows ll rection rtes in the series HOCl + HCl/ HBr supported by different numbers of wter molecules. Wht we cn observe is tht the rections involving HBr re in generl much fster thn the rections involving HCl. In Figure 5B, the mechnism for + H 2 O corresponds to the sme mechnism s for HOCl + HCl + H 2 O (), but we were unble to determine the mechnism corresponding to HOCl + HCl + H 2 O (b). Figure 5D represents the cses for the rections with three wter molecules, which re representtive of n ice surfce. Becuse both rections re lmost brrierless, the temperture dependence is smllsthe HBr rection is lmost independent of temperture chnges, nd the HCl rection chnges only by fctor of 10 in the temperture rnge 190 to 300 K. At 190 K, we observed rection rtes of s -1 nd s -1 for HOCl + HCl nd (n ) 3), respectively. Therefore, the rection-rte difference between the two rections is pproximtely Tble 5 summrizes the trnsmission coefficients t 190 K. Mostly, the smll-curvture tunneling pproch is predominnt over the other forms of tunneling, with some exceptions. For the rection HOCl + 1HCl + 1H 2 O (b) nd lso for the surfcelike rection of HOCl with HCl, LCT clerly predomintes over Figure 5. Rection rtes for the rections of HOCl with HBr. (A), (B), (C), nd (D) represent the rections with n ) 0, 1, 2, nd 3 wter molecules, respectively. Shown re rections with HBr (s) nd HCl ( ). In (B), rection chnnels () nd (b) re shown for the HCl rection, s outlined in the text nd in Figure 2.

7 7856 J. Phys. Chem. A, Vol. 106, No. 34, 2002 Voegele et l. TABLE 5: Trnsmission Coefficients (Tunneling Corrections) for the HOCl + HCl, HBr Rections trnsmission coefficient κ t 190 K HOCl + HCl Wigner LCT SCT n ) n ) 1 () n ) 1 (b) n ) n ) n ) n ) 1 () n ) n ) Most importnt form of tunneling (µomt). T ) 190 K. ll other tunneling pproches. In most cses, the Wigner correction is not sufficient to describe tunneling. The highest tunneling contribution hppens in rections HOCl + HCl + 1H 2 O (b) (representtive of gs-phse rection) nd HOCl + HCl + 3H 2 O (representtive of surfce-ctlyzed rection) with κ s of 113 nd 1.88, respectively. Thus, we cn observe rection-rte enhncements of 113-fold nd 88%, respectively, due to tunneling. The much higher tunneling contribution for 1(b) in comprison to 1() might best be explined by inspecting Figure 1. The curvture of the brrier of chnnel 1(b) is much lrger thn tht for 1(). A detiled inspection showed tht the mechnism of 1() works s follows: First, the proton of HOCl rottes by pproximtely 120 long the Cl-O bond. Next, the two chlorine toms move pproximtely 1.5 Å towrd ech other, thus pproximting the trnsition stte. The smll curvture nd the smll tunneling contribution might be best explined by the strong movement of the two chlorine toms. Compring the gs-phse rections with the surfce-ctlyzed rections, we find tht the rection-rte enhncement is 50 orders of mgnitude. To illustrte this lrge difference, we observe tht the gs-phse rection hppens within billions of yers wheres the surfce-ctlyzed rection hppens within nnoseconds nd femtoseconds. 4. Conclusions In this study, we hve concentrted on the competing rections of HOCl + HCl nd either in the gs phse or on wter clusters representing hexgonl ice surfce. From the methodologicl point of view, we sw tht the trnsition stte for such types of rections is not well described with post Hrtree-Fock methods such s CCSD(T) or QCISD(T) (s in G2 or G3). Therefore, we used the newly developed MPW1K hybrid-dft pproch by Lynch et l., 30 who designed this method especilly to evlute rection brriers. Xu 14 studied the rection of HOCl + HCl + nh 2 O with MP2//HF/6-31G(d) nd found higher brriers throughout nd shorter bond lengths in the hydrogen-bridged wter complexes. When following the minimum-energy pths from the trnsition sttes, we found concerted, synchronous proton trnsfers for ll of the studied systems with no stble intermedite. We determined rection rtes using trnsition-stte theory including tunneling corrections. Clerly, trend of incresing rection rtes by including ctlytic wter molecules in the rection complex ws observed. The unctlyzed gs-phse rection is bout 50 orders of mgnitude slower thn the rection occurring on cluster representing n ice surfce. Tunneling is significnt t bout 190 K becuse it ccelertes the rection on the surfce up to bout 88%. A direct comprison between the HCl nd HBr rections shows tht the HBr rections on the surfce tend to be 3 to 4 orders of mgnitude fster. Considering polr strtospheric clouds of type II, we find tht the rection of HOCl with HBr is the more importnt one s long s the rtio of HBr to HCl is g1:4000. At present strtospheric HCl nd HBr concentrtions, the HBr mechnisms re clerly more importnt. Also, becuse the HBr rection cn occur vi mechnism involving smller rection cluster, the rection hppens under conditions where not enough wter molecules re ccessible for direct prticiption in the rection. After HBr is consumed nd the rtio is <1:4000, the HOCl + HCl rections become predominnt. Acknowledgment. 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